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Model-Theoretic Logics

Author: J Barwise; S Feferman
Publisher: Cambridge : Cambridge University Press, 2017.
Series: Perspectives in logic.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s.  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Barwise, J.
Model-Theoretic Logics
Cambridge : Cambridge University Press,c2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J Barwise; S Feferman
ISBN: 9781316717158 1316717151 9781316749043 1316749045 1316752909 9781316752906
OCLC Number: 983738180
Description: 1 online resource (913 p.).
Contents: Cover ; Half-title ; Series information ; Title page ; Copyright information ; Preface to the Series ; Preface ; Table of contents ; List of Contributors; Part A Introduction, Basic Theory and Examples; Chapter I Model-Theoretic Logics: Background and Aims; 1. Logics Embodying Mathematical Concepts; 1.1. Logic, Structures and Logics; 1.2. The First-Order Thesis ; 1.3. The Completeness Problem; 1.4. Compactness ; 1.5. Mostowski's Proposal and Generalized Quantifiers ; 1.6. Infinitary Logics; 1.7. Second-Order Logic ; 1.8. Applications to Mathematics; 2. Abstract Model Theory 2.1. Lindstrom's Theorem2.2. Characterization Theorems; 2.3. Uses of Abstract Model Theory; 2.4. The Interpolation Theorem and the ∆-Closure; 2.5. Pinning Down Ordinals; 2.6. Hanf Numbers; 2.7. Strong Logics and First-Order Set Theory; 2.8. Other Types of Structures; 2.9. Unnatural Logics; 3. Conclusion; Chapter II Extended Logics: The General Framework; 1. General Logics; 1.1. The Framework; 1.2. Basic Closure Properties; 2. Examples of Principal Logics; 2.1. Logics of Higher Order; 2.2. Examples of Logics with Cardinality Quantifiers; 2.3. Cardinality Quantifiers with Complex Scopes 2.4. Logics with Cofinality Quantifiers2.5. Logics with Quantifiers of Partially Ordered Prefixes; 2.6. Logics with Standard Part; 2.7. Infinitary Logics; 3. Comparing Logics; 3.1. Elementary and Projective Classes; 3.2. A Reduction Method; 4. Lindstrom Quantifiers; 4.1. Definitions and Examples; 4.2. Partial Isomorphisms and a Characterization of L-Equivalence; 4.3. Partially Isomorphic Structures; 5. Compactness and Its Neighbourhood; 5.1. Notions of Compactness; 5.2. Well-Ordering Numbers; 5.3. Substitutes; 6. Lowenheim-Skolem Properties ; 6.1. Hanf Numbers; 6.2. Lowenheim Numbers
Series Title: Perspectives in logic.

Abstract:

This book brings together several directions of work in model theory between the late 1950s and early 1980s.  Read more...

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